It’s hard to say what could be effective.
Dog licences I think would be near impossible to police, from the vetting process to the actual monitoring. Police are already overwhelmed as it is, it (in my eyes) would be hugely unrealistic to add monitoring licences.
Besides, how do you vet a licence in the first place ? I work with animals, and it really is more of a question of responsible training than specific breeds, with exceptions, that aren’t necessarily those that have a huge focus on currently.
Tiny cute dogs can do just as much damage if untrained, all it takes is an unfortunate bite on a child (which would really technically an instinctive fear reaction from the behalf of the dog if they haven’t been socialised and suddenly have a young child running around in proximity : they can’t possibly guess if not socialised adequately that the unfamiliar child wants to pet them).
It as PP posters seems more of a social trend regarding certain breeds of dogs, who can statistically by their size cause more damage.
Unfortunately reinforcing (hopefully temporarily) really huge fines and damages payments to owners could be a deterrent for irresponsible people if incident (I imagine like in many similar law enforcement situations, an evaluation of the dog and owner responsibility could then be carried out), and also leashes at the very least in public places. It is a shame for responsible owners, but that’s the same in many domains.
It’s happening so much more recently and these dogs really have been around for ages, so there is much more likely to be a very huge increased human irresponsibility factor.